Find the length of a rectangular lawn with a perimeter of 32 meters and a width of 5 meters.

Answer:

answer choice C.

Step-by-step explanation:

complementary angles are 2 angles that add up to 90 degrees

90=58+x

90-58=x

x=32

The option a, c, d, e are continuous random variable and option b is discrete random variable.

Discrete variables means countable or finite amount of variables and continuous variables means infinite amount of variables

a. The time for the computer algorithm to assign an image to different categories.

Here,time can have decimal values, so continuous.

b. The no. of bytes used to store a file in the computer.

Here,the number of bytes is never decimal, so discrete.

c. The ozone concentration in µg/m3.

Here the concentration is nothing but quantity and quantity can be decimal value, so continuous.

d. The ejection fraction (volumetric fraction of blood pumped from a heart ventricle with each beat).

Here, volume is a  quantity and quantity can be in decimal value, so continuous.

e. The fluid flow rate in L/min.

Here also the quantity can be in decimal value, so continuous.

Thus, the option a, c, d, e are continuous random variable and option b is discrete random variable.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer:

m = x / n

n = 15

Step-by-step explanation:

Number of chairs per row = m

Number of rows = n

Number of people = x

Number of chairs per row, m = number of people, x / Number of rows, n

m = x / n

If number of attendees, x = 60 ;

Number of chairs per row, m = 4

The number of rows, n = number of attendees / number of chairs per row, m

Hence, n = 60 / 4 = 15 rows

Answer:

Sure! Let’s solve this equation step by step.

(7000).03 + (x).05=830

First, we can simplify the left side of the equation:

210 + 0.05x = 830

Next, we can subtract 210 from both sides:

0.05x = 620

Finally, we can divide both sides by 0.05 to solve for x:

x = 12400

So the solution to the equation (7000).03 + (x).05=830 is x = 12400.

Answer:

88cm^2

Step-by-step explanation:

Area of the rectangle: base x height

Area of parallelogram: base x height

Area of the shaded part: area of rectangle -area of parallelogram:

12x10-4x8=120-32=88

In a single row of yellow, green and red colored tiles, every red tile is preceded immediately by a yellow tile and every yellow tile is preceded immediately by a green tile.

The pattern of color in the row is Green - Yellow - Red - Green - Yellow - Red - Green - Yellow - Red - Green - Yellow - Red and so on...Here, Green and Red will always appear at odd positions and Yellow will always appear at even positions.In order to find the 24th tile in the row, we can first find out the color of tile 23 and 22.23rd tile is Red, as it is preceded immediately by Yellow and Yellow is preceded immediately by Green.22nd tile is Yellow, as it is preceded immediately by Green and Green will appear at all even positions.

Now we know that the 24th tile comes immediately after the 23rd tile which is Red. So the color of the 24th tile will be Green. Hence, the answer is Green.

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Answer:

8 is the correct answer of this question

Answer:

8

Step-by-step explanation:

I will win about $ 59.

This is a question of permutations and combinations.

We know that,

Probability of getting two non face cards = \(\frac{^{40}C_2}{{^{52}C_2}}\) = 10/17

Probability of not getting two non face cards = 1 - (10/17) = 7/17

Hence, we can write,

Money I will get = (7/17)*50*20 =  $ 411.764

Money I'll have to pay = (10/17)*30*20 = $ 352.94

We know that,

Money left with me = Money I will get - Money I'll have to pay

Hence, we can write,

Money left with me =   $ 411.764 - $ 352.94

Money left with me =  58.824 ≈ $ 59

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To prove that for quadratic Bezier curves, the slope of the line segment p0q equals the slope of the tangent line to the curve at p0, and that the slope of the line segment qp1 equals the slope of the tangent line to the curve at p1, we'll use the properties of Bezier curves and their derivatives.

A quadratic Bezier curve is defined by three control points: p0, p1, and p2. The curve is parameterized by a variable t, where t ranges from 0 to 1. The equation for the quadratic Bezier curve is:

B(t) = (1 - t)^2 * p0 + 2 * (1 - t) * t * p1 + t^2 * p2

Let's calculate the derivative of the Bezier curve with respect to t, denoted as B'(t):

B'(t) = d/dt [(1 - t)^2 * p0 + 2 * (1 - t) * t * p1 + t^2 * p2]

= -2 * (1 - t) * p0 + 2 * (1 - 2t) * p1 + 2 * t * p2

= -2 * (1 - t) * p0 + 2 * (1 - 2t) * p1 + 2 * t * p2

Now, let's find the slope of the line segment p0q, where q is any point on the curve. We'll substitute t = 0 into the equation of the Bezier curve:

q = B(0) = (1 - 0)^2 * p0 + 2 * (1 - 0) * 0 * p1 + 0^2 * p2

= p0

Therefore, q = p0.

The slope of the line segment p0q is given by the difference in y-coordinates divided by the difference in x-coordinates:

slope_p0q = (q.y - p0.y) / (q.x - p0.x)

Since q = p0, the numerator becomes 0, and the slope of the line segment p0q becomes 0.

Now, let's find the slope of the tangent line to the curve at p0. We'll substitute t = 0 into the equation for the derivative of the Bezier curve:

B'(0) = -2 * (1 - 0) * p0 + 2 * (1 - 2 * 0) * p1 + 2 * 0 * p2

= -2 * p0 + 2 * p1

The slope of the tangent line to the curve at p0 is given by the y-component divided by the x-component of the derivative at t = 0:

slope_tangent_p0 = (B'(0)).y / (B'(0)).x

= (-2 * p0 + 2 * p1).y / (-2 * p0 + 2 * p1).x

Since we have q = p0, we can simplify the expression:

slope_tangent_p0 = (-2 * q + 2 * p1).y / (-2 * q + 2 * p1).x

Now, let's find the slope of the line segment qp1. We'll substitute t = 1 into the equation of the Bezier curve:

q = B(1) = (1 - 1)^2 * p0 + 2 * (1 - 1) * 1 * p1 + 1^2 * p2

= p2

Therefore, q = p2.

The slope of the line segment qp1 is given by the difference in y-coordinates divided by the difference in x-coordinates:

slope_qp1 = (p2.y - q.y) / (p2.x - q.x)

Since q = p2, the numerator becomes 0, and the slope of the line segment qp1 becomes 0.

Now, let's find the slope of the tangent line to the curve at p1. We'll substitute t = 1 into the equation for the derivative of the Bezier curve:

B'(1) = -2 * (1 - 1) * p0 + 2 * (1 - 2 * 1) * p1 + 2 * 1 * p2

= 2 * p2 - 2 * p1

The slope of the tangent line to the curve at p1 is given by the y-component divided by the x-component of the derivative at t = 1:

slope_tangent_p1 = (B'(1)).y / (B'(1)).x

= (2 * p2 - 2 * p1).y / (2 * p2 - 2 * p1).x

Since we have q = p2, we can simplify the expression:

slope_tangent_p1 = (2 * q - 2 * p1).y / (2 * q - 2 * p1).x

As we can see, both slope_p0q and slope_tangent_p0 are equal to 0, and both slope_qp1 and slope_tangent_p1 are equal to 0.

Therefore, we have proved that for quadratic Bezier curves, the slope of the line segment p0q equals the slope of the tangent line to the curve at p0, and the slope of the line segment qp1 equals the slope of the tangent line to the curve at p1.

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Step-by-step explanation:

I don't see the answer options.

but in line 3 this is simply done by multiplying to eliminate the fractions on the right side of the equations.

and so, since h = h, we get c×sin(B) = b×sin(C).

in the last line we divide both sides first by b and then by c and get

sin(B)/b = sin(C)/c

the law of sine ...

Answer: Sarah got 95 percent on her test

Step-by-step explanation:

The true solutions are" The value of W cannot be a negative number ", "substitution is used to replace the variable l with a value of 20"  and " the subtraction property of equality is used to isolate the term with the variable W

Given that Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet .she writes and solves the equation 2l+2w=62 to find the width of the run and asked what are the true solutions

⇒2l+2w= 62

⇒2w+2(20)=62  ( given the length to run is 20 feet)

⇒2w= 62-40

⇒2w=22

⇒w=11

The value of w is 11 feet .so, 1st statement is false and statement 2 is also false. 11 feet is not a negative number so, the 3rd statement is correct. given the length to run is 20 feet, substitution is used to replace the variable l with a value of 20 i.e. 4th statement is correct. To find the value of w, used subtraction property i.e. 4th statement is also correct

Hence, The true solutions are" The value of W cannot be a negative number ", "substitution is used to replace the variable l with a value of 20"  and " the subtraction property of equality is used to isolate the term with the variable W "

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The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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Answer:

x=20

Step-by-step explanation:

2.5x=50

\(\frac{2.5}{2.5} =\frac{50}{2.5}\)

x = 20

Have a great day!!!!

PumpkinSpice1

the solution to the equation 2.5x = 50 is x = 20.

To solve the equation 2.5x = 50 and find the value of x, we can divide both sides of the equation by 2.5. By doing so, we eliminate the coefficient of x and isolate the variable.

Dividing both sides by 2.5, we have:

(2.5x) / 2.5 = 50 / 2.5

Simplifying, we get:

x = 20

Therefore, the solution to the equation 2.5x = 50 is x = 20. When we substitute x with 20 in the equation, we have 2.5 * 20, which indeed equals 50. Thus, x = 20 satisfies the equation, and it represents the value that makes the equation true.

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Answer:

  a) m = 60°, n = 30°

  b) m = 20°, n = 45°

Step-by-step explanation:

The top and bottom horizontal lines are parallel, so angle m is an alternate interior angle congruent to the interior angle(s) of the equilateral triangle. Those angles are all 60°.

Angle n is the complement of angle m, so is 90°-60° = 30°

  m = 60°, n = 30°

__

The base angles of the isosceles right triangle are n = 45°. (This should be a memorized fact. It is computed as (180° -90°)/2 = 45°.)

The base angles of the isosceles acute triangle are (180°-50°)/2 = 65°. Angle m is the difference between one of these and angle n.

  m = 65° -45° = 20°

  m = 20°, n = 45°

_____

Additional comment

The sum of angles of a triangle is 180°. The "base" angles of an isosceles triangle (one with two equal sides) are equal. If 'a' is the third angle, and 'b' are the base angles, you have ...

  a + 2b = 180°

  2b = 180° -a

  b = (180° -a)/2 . . . . . . the relation used above

The mean and standard deviation of the population is 19.8 and 0.004 respectively.

Mean:

The mean is the simple mathematical average of a set of two or more numbers. The mean of a given set of numbers can be calculated in several ways, including the arithmetic mean, which uses the sum of the numbers in the range, and the geometric mean, which takes the mean product of a set. However, all major methods of calculating simple averages produce the same approximate result most of the time.

Standard Deviation:

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values.  A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

Given that:

E(x) = μ = 19.8

var(x) = σ²/n = 0.2/50 = 0.004

from here can say that mean = 19.8 and

standard Deviation is 0.004.

Now,

295 -298 P(Bottle x < 295) =P(Z< ) =-1.00 =.15873

Thus, there is nearly a 16% probability that just 1 randomly selected

bottle contains < 295 ml.

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Answer:

answer is 7.66666 so the answer is between 7 and 8

Step-by-step explanation:

The next number in the pattern will be 44. Then the correct option is D.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The pattern is given below.

4, 6, 11, 19, 30,

The pattern is given as,

4 + 2 + 3 x 0 = 6

6 + 2 + 3 x 1 = 11

11 + 2 + 3 x 2 = 19

19 + 2 + 3 x 3 = 30

30 + 2 + 3 x 4 = 44

The next number in the pattern will be 44. Then the correct option is D.

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Answer:

Well, P(Monday)= 1/7 = 14.3%

P(starts with S)= 2/7 = 28.6%

P(Monday or starts with S)= 3/7 = 42.9%

Step-by-step explanation:

Have a good day!!!

The probability of choosing Monday is,

P = 1 / 7

And, the probability of choosing starts with S is,

P = 2/7

And, the probability of choosing Monday or starts with S is,

P = 3/7

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A day of the week is randomly chosen.

Since, Number of days in a week = 7

Hence, the probability of choosing Monday is,

P = 1 / 7

And, the probability of choosing starts with S is,

P = 2/7

So, the probability of choosing Monday or starts with S is,

P = 2/7 + 1/7

P = 3/7

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The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3).


To find the lower bound, we need to determine the term with the highest growth rate in the function f(n). In this case, the highest growth rate is determined by the cubic term 4n^3. The other terms, 2n^2 and n, have a lower growth rate, and therefore, their impact on the overall growth of the function becomes less significant as n increases.

As a result, we can say that the lower bound for the function f(n) is dominated by the cubic term 4n^3, which means that the function f(n) grows at least as fast as Ω(n^3).


The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3). This means that the function grows at least as fast as a cubic function, and the other terms have a lesser impact on the overall growth rate as n increases.

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The correct answer is- we can be 99% confident that the true mean waiting time is between 4.16 and 12.84 minutes.

A doctor took a random sample of n = 6 patients to see how long they each spent in the waiting room. She wants to construct a t interval for the mean waiting time with 99% confidence. The times in the sample were roughly symmetric with a mean of z = 8.5 minutes and a standard deviation of sx = 2.8 minutes. We have to find the 99% confidence interval of the waiting time.

The formula for the confidence interval is shown below:\(\[\large \bar x-t_{\alpha/2}\frac{s}{\sqrt{n}} < \mu < \bar x+t_{\alpha/2}\frac{s}{\sqrt{n}}\]\)

Where: \(\[\large \bar x\]\) is the sample mean \(\[s\]\) is the sample standard deviation \(\[n\]\) is the sample size\(\[\large t_{\alpha/2}\]\) is the t-score from the t-distribution with (n - 1) degrees of freedom, where α is the level of significance

The sample mean is\(\[\large\bar x=8.5\]\) and the sample standard deviation is \(\[\large s=2.8\].\)

Since the sample size is small, we must use a t-distribution with n - 1 degrees of freedom. With 99% confidence, α = 0.01/2 = 0.005.

Using a t-table for 5 degrees of freedom and α = 0.005, we get\(\[\large t_{\alpha/2}\] = 4.032.\)

On substituting the values, we get the interval as shown below: \(\[\large 8.5-4.032\frac{2.8}{\sqrt{6}} < \mu < 8.5+4.032\frac{2.8}{\sqrt{6}}\]\)

The confidence interval is (4.16, 12.84).

Therefore, we can be 99% confident that the true mean waiting time is between 4.16 and 12.84 minutes

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Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Answer:

Maximum: 756

Minimum: 600

Step-by-step explanation:

A square is the shape that has the maximum area out of all possible rectangles of a given perimeter. This means that to create the maximum value of P, you will want the two parentheses to be as close in value as possible, and to create the minimum value, for them to have the biggest difference. 1+2+3...+10=55, which is not even, but can be divided as closely as possible into 27 and 28, which have a product of 756. This can be done in this problem in several ways, one of which is:

(1+3+5+8+10)(2+4+6+7+9)

For the minimum, the largest difference can be made when one term is full of the smallest numbers, and the other is full of the largest, or:

(1+2+3+4+5)(6+7+8+9+10)=600

Hope this helps!

The order of the colors is Red, blue, yellow

Chromatography is a laboratory technique used to separate and analyze mixtures of different compounds based on their physical and chemical properties. It involves passing a mixture through a stationary phase, which may be a solid or a liquid, and a mobile phase, which may be a liquid or a gas.

As the mixture passes through the stationary phase, the different compounds in the mixture interact with the stationary phase to varying degrees, causing them to separate. The mobile phase carries the separated components through the stationary phase, and the separated components are detected and analyzed using a detector, such as a spectrophotometer.

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Answer:

£18,810 is the amount of rent Pippa paid in 2017.

Step-by-step explanation:

This is percentage increase:

(100+14)% = 114%

£1650 × 114%

= £1,650 × 114/100

= £18,810